Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem

Cañas, Gustavo; Etcheverry, Sebastián; Gómez, Esteban S.; Saavedra, C.; Xavier, G. B.; Lima, G.; Cabello, Adán

doi:10.1103/physreva.90.012119

Cited by 34 publications

(34 citation statements)

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“…In 1995 Kernaghan and Peres produced a 36-11 KS critical set and a 40-25 non-critical one (experimentally implemented in [26]) from which several smaller ones including 36-11 can be obtained [43]; in 2006 Ruuge and van Oystaeyen gave a scheme for constructing 8-dim KS proofs but did not themselves construct any [55]; in 2012 Ruuge claimed to have given an example of a 36-vertex 8-dim KS set [34] but we were not able to identify its octads of orthogonal vertices in [34] (nor to contact him), so, we could not verify whether it is isomorphic to 36-11 from [43] as claimed in [34]); and finally, also in 2012, Planat discussed 8-dim KS sets that can be obtained from the Kernaghan-Peres' 40-25 KS set [56]. In 2015 Waegell and Aravind obtained a KS master set with 120 vertices and 2025 edges and, from it, many smaller 8-dim KS sets, including non-critical Kernaghan-Peres' 40-25 one [57] (see also [58]).…”

Section: -2024 Class Of 8-dim Ks Sets Andmentioning

confidence: 99%

“…They were implemented for 4-dim systems with photons [13][14][15][16][17][18], neutrons [19][20][21] trapped ions [22], and molecular nuclear spins in the solid states [23], for 6-dim systems via six path possibilities for the photon transmission through a diffractive aperture [24,25], and for 8-dim systems by means of the linear transverse momentum of single photons transmitted by diffractive apertures addressed in spatial light modulators [26].…”

Section: Introductionmentioning

confidence: 99%

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Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Pavičić¹

2017

Phys. Rev. A

124

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Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both for theoretical considerations and for experimental implementation to find new types and instances of contextual sets and develop methods of their optimal generation. We present an arbitrary exhaustive hypergraph-based generation of the most explored contextual sets-Kochen-Specker (KS) ones-in 4, 6, 8, 16, and 32 dimensions. We consider and analyse twelve KS classes and obtain numerous properties of theirs, which we then compare with the results previously obtained in the literature. We generate several thousand times more types and instances of KS sets than previously known. All KS sets in three of the classes and in the upper part of a fourth are novel. We make use of the MMP hypergraph language, algorithms, and programs to generate KS sets strictly following their definition from the Kochen-Specker theorem. This approach proves to be particularly advantageous over the parity-proof-based ones (which prevail in the literature), since it turns out that only a very few KS sets have a parity proof (in six KS classes < 0.01% and in one of them 0%). MMP hypergraph formalism enables a translation of an exponentially complex task of solving systems of nonlinear equations, describing KS vector orthogonalities, into a statistically linearly complex task of evaluating vertex states of hypergraph edges, thus exponentially speeding up the generation of KS sets and enabling us to generate billions of novel instances of them. The MMP hypergraph notation also enables us to graphically represent KS sets and to visually discern their features.

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Section: -2024 Class Of 8-dim Ks Sets Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Pavičić¹

2017

Phys. Rev. A

124

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“…In the final part of the setup, a "pointlike" avalanche single-photon detector (APD) with a 10 µm pinhole is placed at the center of the far field plane of the SLM4. In this case, the probability of single-photon detection P (x, x 0 , y, b) is proportional to | ϕ y,b |ψ x,x0 | 2 [45][46][47][48]. However, since for each d one of the targeted protocol measurements is rank-two projective (see Append.…”

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confidence: 99%

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

et al. 2018

Self Cite

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Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission and measurement of a single quantum system; in other words quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realise such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the post-quantum Bell correlations obeying only locality in the macroscopic limit. Surprisingly, we find that the advantages are tied to the use of measurements that are not rank-one projective. We provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.Introduction.-Communication complexity problems (CCPs) are tasks in which distant parties hold local data, the collection of which is needed for a computation of their interest. To make the computation possible, the parties communicate with each other. However, the amount of communication is limited and therefore not all data can be sent. The CCP consist in parties adopting an efficient communication strategy which allows them to perform the desired computation with a probability as high as possible. Efficient use of quantitatively limited communication is a broadly relevant matter [1], which provides fundamental insights on physical limitations [2,3].The ability to process information depends on the choice of the physical system into which the information is encoded [4]. Consequently, quantum entities without a classical counterpart can be regarded as tools for quantum information processing. The most famous example is entanglement. In a quantum CCP, parties may share an entangled state on which they perform local measurements, generating strongly correlated data which violates a Bell inequality. That data can then be used to assist a classical communication strategy [5]. In fact, Bell inequalities have been systematically linked to CCPs [6-8], and their violation enables better-than-classical communication efficiencies [7][8][9][10][11][12][13][14][15].Nevertheless, quantum theory presents also a second approach to CCPs: substituting classical communication with quantum communication. The justification for such a substitution relies on the Holevo theorem [16] which implies that no more information can be extracted from quantum d-level system than from a classical d-level system. Hence, in a quantum communication strategy, information is encoded in a quantum state of a specified Hilbe...

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“…A series of experimental implementations of 4D KS sets have been carried out recently, using photons [1][2][3][4][5][6], neutrons [7][8][9], trapped ions [10], and solid state molecular nuclear spins [11]. Sets in 6D have been implemented via six paths [12,13] and in 8D using photons [14].…”

Section: Introductionmentioning

confidence: 99%

Automated generation of Kochen-Specker sets

Pavičić

Waegell

Megill

et al. 2019

Sci Rep

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Quantum contextuality turns out to be a necessary resource for universal quantum computation and also has applications in quantum communication. Thus it becomes important to generate contextual sets of arbitrary structure and complexity to enable a variety of implementations. In recent years, such generation has been done for contextual sets known as Kochen-Specker sets. Up to now, two approaches have been used for massive generation of non-isomorphic Kochen-Specker sets: exhaustive generation up to a given size and downward generation from master sets and their associated coordinatizations. Master sets were obtained earlier from serendipitous or intuitive connections with polytopes or Pauli operators, and more recently from arbitrary vector components using an algorithm that generates orthogonal vector groupings from them. However, both upward and downward generation face an inherent exponential complexity barrier. In contrast, in this paper we present methods and algorithms that we apply to downward generation that can overcome the exponential barrier in many cases of interest. These involve tailoring and manipulating Kochen-Specker master sets obtained from a small number of simple vector components, filtered by the features of the sets we aim to obtain. Some of the classes of Kochen-Specker sets we generate contain all previously known ones, and others are completely novel. We provide examples of both kinds in 4- and 6-dim Hilbert spaces. We also give a brief introduction for a wider audience and a novice reader.

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Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem

Cited by 34 publications

References 28 publications

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

Automated generation of Kochen-Specker sets

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